Polarizability and Effective Permittivity of Layered and Continuously Inhomogeneous Dielectric Ellipsoids

In this paper, the polarizabilities of partially and continuously inhomogeneous dielectric ellipsoids are analyzed. Multilayer inclusions where the boundaries between the layers are confocal ellipsoids, are solved in a static field. Transmission line analogy is applied, resulting in matrices with which the field components and the polarizability can be solved. In case of the continuous permittivity profile, a differential equation is derived for the scattered potential, and from the amplitude of this function, the polarizability results. The limitation in the continuous case is that the permittivity function of the ellipsoid depend only on one coordinate (ξ) in the ellipsoidal coordinate system. The theory is applied to calculating the microwave attenuation of melting hail at the frequency of 1 GHz, where the hydrometeors are modeled as two-layer ellipsoids.